Many channel models proposed for wireless communication systems characterize the channel impulse response (CIR) as being sparse in the delay domain, i.e. a sum of a few dominant multi-path components, each associated with a delay and a complex gain. Based on this channel property, estimation techniques employing compressed sensing and sparse channel representations may be used to reconstruct the channel. However, the channel observed by the receiver may include the wireless propagation channel together with other effects at the transmitter and receiver side, such as antenna responses or non-ideal pulse-shaping transceiver filters. Due to these effects, the overall channel as seen by the receiver might not be purely sparse in the delay domain. In reality, the CIR experienced at the receiver may be a composite response that includes, in addition to the true CIR, the CIRs of the OFDM (Orthogonal Frequency Division Multiplex) RF (Radio Frequency) transmit (TX) and receive (RX) shape filters. The RF shape filters may interact with the coefficients of the true CIR, e.g. by introducing a leakage in the composite CIR around the true components of the CIR. For example, in LTE (Long Term Evolution) systems, this effect may be significant given the typical transmission bandwidth on the order of 10 MHz.